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Differential Equations Lecture Work Solutions 96

# Differential Equations Lecture Work Solutions 96 - < y<...

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4.3 Vibrations of a rectangular Membrane Problems 1. Solve the wave equation u tt ( x, y, t ) = c 2 ( u xx ( x, y, t ) + u yy ( x, y, t )) , on the rectangle 0 < x < L, 0 < y < H subject to the initial conditions u ( x, y, 0) = f ( x, y ) , u t ( x, y, 0) = g ( x, y ) , and the boundary conditions a. u (0 , y, t ) = u x ( L, y, t ) = 0 , u ( x, 0 , t ) = u ( x, H, t ) = 0 . b. u (0 , y, t ) = u ( L, y, t ) = 0 , u ( x, 0 , t ) = u ( x, H, t ) = 0 . c. u x (0 , y, t ) = u ( L, y, t ) = 0 , u y ( x, 0 , t ) = u y ( x, H, t ) = 0 . 2. Solve the wave equation on a rectangular box 0 < x < L,
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Unformatted text preview: < y < H, < z < W, u tt ( x, y, z, t ) = c 2 ( u xx + u yy + u zz ) , subject to the boundary conditions u (0 , y, z, t ) = u ( L, y, z, t ) = 0 , u ( x, , z, t ) = u ( x, H, z, t ) = 0 , u ( x, y, , t ) = u ( x, y, W, t ) = 0 , and the initial conditions u ( x, y, z, 0) = f ( x, y, z ) , u t ( x, y, z, 0) = g ( x, y, z ) . 96...
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